Question: One digit of the decimal representation of $\frac{5}{7}$ is randomly selected. What is the probability that the digit is a 4? Express your answer as a common fraction.
Solution: The decimal representation of $\frac{5}{7}$ is $0.\overline{714285}$, which has a repeating block of 6 digits. Since 4 is one of those six digits that keep repeating, the probability that the selected digit is a 4 is $\boxed{\frac{1}{6}}$.